Known as "the glass house", the building, designed in 1980 by Mason and Wales architect Ashley Muir, won an enduring architecture award at the 2021 New Zealand Institute of Architects southern branch awards.
Soon, it will be cleared for operational space at the port, Port Otago chief executive Kevin Winders said.
"It’s a piece-by-piece deconstruction," Mr Winders said.
"At the moment, they’ve got the teams working on the ground floor and the middle floor to strip out all the internal partitions and all the framing.
"Then they’ll move forward to pick all the glass and scaffolding up and pull it apart — and ultimately, they’ll come in with the bigger gear and start to pull down and eat through the concrete blocks and the pillars that hold up the building.
"It’ll be a progressive project over about the next six weeks."
The gatehouse, the smaller building between the glass house and the historic Port Chalmers Maritime Museum’s new expansion, was also being removed.
The site was expected to be cleared by Christmas.
For at least the next 12 months the area would be used to process containers, Mr Winders said.
"We’ll look at what we do in the future, but it’s a handy bit of real estate that we’ll be using productively for the container terminal."
Work continued across the street in the museum expansion.
The annex, at the back of the structure, where the port company housed its administration team, was already operational.
However, contractors from Calder Stewart remained inside the museum, completing the fit out, Mr Winders said.
Most of that work would be completed in the next month, he said.
At that stage the project would be handed over to the museum team. A "really nice, new vibrant maritime museum" was expected to open about March, Mr Winders said.